reconstitute spatial weights matrix...

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BESSH-16

RECONSTITUTE SPATIAL WEIGHTS MATRIX CONSIDERING U-CITY

NETWORK STRUCTURE

SUNGHWAN KIM1, KABSUNG KIM2*

1,2,3Yonsei University, South Korea

Keywords: Spatial Weights matrix (SWM)

Spatial Lag Model (SLM)

Housing Sales Price, Seoul

U-City

Abstract. In this study, we reconstitute a spatial weights matrix for U-City Network Structure and construct a

regression-based spatial analysis model among 16 major administrative areas. Existing spatial weight matrices

for spatial autoregressive models commonly consider adjacency or invert distance weighting. However,

nowadays, a virtual network system is more important than actual distance to reveal spatial dependencies.

Especially in Korea, U-City(or smart city) network structures have expanded rapidly by the government and

reconstructed traditional urban systems. The most characteristic point from advanced research is that we

consider the U-City network structure into the spatial adjacencies and interactions model. This result in a family

of spatial OD models that represent an extension of the spatial regression models described in Anselin(1988).

INTRODUCTION

-CITY(UBIQUITOUS CITY), the Korean smart city model, was

made to take advantage of the developed Korea‟s Information

technology(IT) infrastructure and to make urban management

easier such as disaster prevention and crime prevention. U-City

projects in Korea have been operated by government test-bed

projects and are underway to build a nationwide (MOLIT, 2013).

In particular among the projects, CCTV integrated management

service to take care of crime-ridden districts getting responses

from people. The most important reason for attracting attention to

U-City is the concept of „physical distance‟ is weakening.

Because older cities are now changing into IT infrastructure basis

management environment.

Housing sales price, a research subject of this study, can also be

seen evolving change pattern with U-City system. Since housing

fixes on the land, it has a unique feature that cannot move. Thus,

house sales prices have not been determined independently and

usually formed by exchange influences among the neighbored

regions; it is widely accepted theory(Park and Ahn, 2005; Gillen

et al., 2001). However, housing prices so that Park and

Kim(2007) has pointed out, sometimes showing another

correlation with it other than neighboring or physical distance. As

a typical example on Seoul, house sales prices in the Gangnam-gu

affects the Mokdong and Jamsil area nearly without delay. Look

at this on the basis, in addition to the regional neighbor and

* Corresponding author: Kabsung Kim

E-mail: [email protected]

distance, several other influential acts believed to form the house

prices.

Figure 1. An outline map of the research area(Seoul, Korea)

U

Kabsung Kim /BESSH--2016/Full Paper Proceeding Vol No-76, Issue 3, 35-45

International Conference on “Business Economics, Social Science & Humanities” BESSH-2015

36

In this study, to recognize the fact that such changes in the U-City

and another urban model is likely to affect home sales, new

spatial weights matrix (SWM) that can reflect the influence would

like to propose. In addition, we have been studying with an

emphasis on understanding the statistical significance and

efficiency of the new SWM.

THEORETICAL DISCUSSIONS AND PREVIOUS

RESEARCHES

Studies in regards to real estate values have generally taken two

theoretical flows. While one flow follows the equilibrium price

model based on the law of demand and supply, another one

centers around the hedonic price model by Lancaster (1966) and

Rosen (1974).

The hedonic price model argues that the purchase of any good

signifies the purchase of the entire good, including its inherent

characteristics, and thus the price of a good is decided by its

quantity and inherent characteristics. The hedonic price model is

useful for a wide research subject as it can analyze the various

elements affecting real estate prices. Within these logical

boundaries, statistical methods such as regression models were

applied to take into consideration the various characteristic of a

house including generational, regional, and apartment-specific

features. Of the various characteristics, the environmental element

was studied in regards to unwanted public facilities such as trash

incineration facilities (Cho, 1998) or detention centers and

electricity substations (Choi et al, 2000) and their effects on the

real estate prices. Preceding researches that studied real estate

prices caused by social environmental

changes from public rental housings also applied these methods

(Woo, 2005; Moon et al, 2006; Hwang, 2009).

Studies that follow the hedonic price model evolved alongside the

development of improved statistical instruments. The most

notable case is the use of hierarchical linear model. Hedonic price

model fundamentally applies several variables of different levels

including generational, regional, and apartment-specific features.

Naturally, as it provides the most suitable tool for analyzing the

variables, hierarchical lineal model has been frequently used in

recent real estate price researches based on hedonic price model

(Kim, 2003; Kim et al, 2004; Choi et al, 2004; Jung, 2006; Lee et

al., 2012; Yoon et al., 2012). Another recurrently attempted tool

is the spatial regression analysis, which can take spatial

autocorrelation into consideration (Choi et al, 2003; Oh et al,

2014). These attempts are results of the due to the immobility of

the real estate, which necessitates control over the real estate

prices‟ spatial autocorrelation.

On the other side, about an SWM, there is also extensive

literature. When it is first introduced by Anselin (1988), there are

only a few generating methods utilizing adjacent or distance

several generation methods exist. The simplest types of SWM are

contiguity type matrices. However, over time, new generation

methods have been developed. Getis and Aldstadt (2004)

suggested over a dozen different types of SWM. Nowadays, the

geo-statistical method is known as the most complex type. In

between these differences are a host of different distance-related

functions. Matters should focus on the debate on SWM is not a

using complex or advanced method but specifying how research

object is located in space concerning the other reference object.

There are 3 types of considerations and viewpoints when making

SWM (Aldstadt and Getis, 2006):

1. “A theoretical notion of spatial association, such as a

distance decline function.”

2. “A geometric indicator of spatial nearness, such as a

representation of contiguous spatial units.”

3. “Some descriptive expression of the spatial association

within a set of data, such as an empirical variogram

function.”

In consideration of the above three perspectives on generating

SWM, this study focuses on the third viewpoint. Because

viewpoints 3 is more proper way than the others, perhaps. It can

be proved in descriptive analysis and phenomenon-based

researches.

PHENOMENON-BASED RESEARCH

Data Acquisition

The data used in this study can be divided mainly into two types.

At first, the actual transaction data for calculating home sales was

provided by「 The Actual Acquisition Price of Real Estate

Information System」 which operates in MOLIT. In contrast to

previous studies (Park and Kim, 2007; Lee and Park, 2013), the

actual transaction data is used in the present study. Thus, it is

expected to be a more sophisticated analysis can be done by

reflecting the real price, not a call price. Data included three

months from October to December 2015, and the total 19,131

sales data were collected. Data covered Seoul, Korea.



37

TABLE I

THE RESULT OF DESCRIPTIVE ANALYSIS

Variables Measure Mean SD Min. Max

Dependent

Variables

(total 14

variables)

Physical

Characteristics

(total 10

variables)

Total Area ㎡ 112.14 34.09 15.00 350.50

Rebuilding is

Scheduled

Yes(%) 0.01 0.09 - -

Total Buildings 5.32 8.11 1.00 74.00

Area for Exclusive Use ㎡ 78.50 28.48 11.96 270.25

Num. of Rooms 2.88 0.79 1.00 7.00

Num. of Baths 1.52 0.57 1.00 3.00

Total Household 412.82 548.98 45.00 5,540.00

Parking Lot/HH 1.20 0.49 0.30 5.80

Porch Cascade

Type

0.63 0.37 - -

Aging of Apts. Years 12.38 9.18 0.00 36.00

Environmental

Characteristics

(total 4 variables)

Dist. to General

Hospital

Meters 1,732.15 812.33 133.86 4,552.27

Dist. to Primary School Meters 452.31 223.57 78.52 1,243.54

Dist. to High School Meters 720.94 391.08 52.22 3,005.38

Dist. to Subway Station Meters 635.30 262.41 42.29 2,802.51

U-City Available Yes(%) 44.00 0.13 - -

Independent

Variable KRW/㎡ 10thou.

KRW 653.00 289.80 178.00 3,064.00

TABLE II

THE AVERAGE PRICES OF HOUSING SALES PRICES

Administrative Districts Prices (in million KRW)

Gangnam 1010

Seocho 1004

Yongsan 832

Songpa 714

Mapo 627

Gwangjin 606

Jung 564

Seongdong 553

Jongno 551

Yangcheon 528

Dongjak 517

Gangdong 485

Yeongdeungpo 457

Seongbuk 418

Dongdaemun 404

Seodaemun 394

Gangseo 384

Eunpyeong 374

Gwanak 371

Gangbuk 348

Guro 344

Jungnang 315

Geumcheon 315

Nowon 297

Dobong 279

* Price : High to Low



38

Figure 2. Apartment distribution map of the research area

Then, the building register to obtain the co-housing estates

information was constructed in the database. This data was

processed download from the large-capacity data providing

system of "Architectural Information Open System", which

operates in MOLIT. The building that has been registered as a

"co-housing" in the construction in the December 2015 criteria

Seoul, a total 96,603 buildings and this is a value except for the

duplicates.

Next, it was processed and join in the parcel number unit (PNU)

code for the purpose of trying to analyze together the actual

acquisition price information and information of the co-residential

complex to prepare for those mentioned above. Matching rate is

100%, all of the information has been fully joined.

Finally, to calculate the other environmental variables, get the

(X, Y) coordinates of subway stations and bus stops from

geographic information system (GIS) shape file. Make the GIS

spatial operations utilization to analyze the traffic environment,

the educational environment, and the living environment.

Basic statistics of data obtained through these process is as

<Table 1> below. Which is a feature that was the rebuilding

related variable is added that is not described in the previous

variable explanation. According to the Park and Kim (2007),

general buildings prices decline gradually over time because the

life expectancy due is approaching, but the apartments prices are

not when if reconstruction plan exists. Therefore, after the

„reconstruction plan‟ variable has inserted as a control value, then

the analysis was performed.

Graphical Analysis

As a result of comparing the distinction apartment sale price, it

has been derived as <Table 2>. Gangnam shows highest average

sale price in Seoul, and then Seocho, Songpa, and Yongsan form

high price group. Nowon has lowest mean sales price, and then

Dobong, Geumcheon, and Eunpyeong join small price group. The

average sale price difference between Dobong District(showed

the lowest cost, 279 million KRW) and Gangnam-gu, showed the

highest amount of money (1,010 million KRW) was found to be

up to about 3.6 times.

After a visual analysis of time-series change over the study

period, the graphs in the fourth quarter of 2015 showed that draws

a steady graph does not cause noticeable changes. Therefore, it

can be analyzed by the cross-sectional method to derive the mean

quarterly without including the features of the time-series data.

The distinct feature is that buying and selling price has a

downward trend in the Gangseo (Magok district), which is

expected to intensive housing supply in the future (about a year).

For the reason of this trend appeared, Magok district has lots of

long-term periods chonsei housing and public rental housing, so it

has an adverse impact on the price in the vicinity of the apartment

(Kim et al, 2015).

Correlation Test

It was carried out correlation test to explain the similarity of these

distinctions sale price movement statistically. First of all, looking

at the area that showed a high correlation, Seocho-Gangnam-

Sangpa region, as we saw in the previous graphical situation

analysis had been given a strong influence each other. This

influence could be explained by the proximity of the group.

However, when seen in the reference to the Gangnam, it was

found that has signed Yangcheon, Yeongdeungpo, a high

correlation also Nowon. Despite the considerable distance away

from each region, it seems to be having an unknown impact in

determining the sale price fluctuations and some relationships

between each sphere.



39

Figure 3. Correlation map with Gangnam and the others

The Yangcheon District that shows the distinctive look.

Yangcheon, as seen in the following <Figure 4>, in addition to

the Mapo and Yeongdeungpo, which are adjacent to each other

and also appeared receive affecting both Gangnam and Seocho.

This seems to be due to Mokdong Newtown is located in the

Yangcheon. Mokdong is a large-scale apartment complex that has

been construction in 1985-1988, and forms a high level of house

prices in the Yangcheon as education fever is a very high.

Because Gangnam•Seocho shares with this feature and is

estimated that show such a correlation. That it might seem that

the correlation and also due to some other influence, except for

the fact that geographical proximity can see in the example

Yangcheon.

Figure 3. Correlation map with Yangcheon and the other

Margareth Gfrerer /BESSH--2016/Full Paper Proceeding Vol No-76, Issue 3, 1-10


Full result of correlation test is as follows <table 3>.

* GN : Gangnam, SC : Seocho, YS : Yongsan, SP : Songpa, MP : Mapo, GJ : Gwangjin, JU : Jung, SD : Seongdong, JO : Jongno, YC : Yangcheon, DJ : Dongjak GD : Gangdong, YP : Yeongdeungpo, SB : Seongbuk, DM : Dongdaemun, SM :

Seodaemun, GS : Gangseo,

EP : Eunpyeong, GA : Gwanak, GB : Gangbuk, GR : Guro, JN : Jungnang, GC : Geumcheon, NW : Nowon, DB : Dobong

TABLE III THE RESULT OF CORRELATION TEST

THE RESULT OF CORRELATION TEST GN SC YS SP MP GJ JU SD JO YC DJ GD YP SB DM SM GS EP GA GB GR JN GC NW DB

GN 1.00

SC 0.97 1.00

YS 0.66 0.71 1.00

SP 0.95 0.97 0.61 1.00

MP 0.56 0.59 0.93 0.55 1.00

GJ 0.81 0.77 0.61 0.78 0.42 1.00

JU 0.38 0.43 0.92 0.44 0.65 0.51 1.00

SD 0.72 0.68 0.42 0.65 0.48 0.66 0.38 1.00

JO 0.55 0.64 0.73 0.57 0.82 0.36 0.82 0.47 1.00

YC 0.91 0.88 0.69 0.84 0.86 0.75 0.29 0.67 0.42 1.00

DJ 0.86 0.91 0.87 0.81 0.77 0.78 0.29 0.65 0.49 0.91 1.00

GD 0.66 0.65 0.31 0.64 0.51 0.33 0.28 0.45 0.24 0.37 0.39 1.00

YP 0.91 0.89 0.73 0.86 0.89 0.71 0.54 0.70 0.45 0.94 0.86 0.35 1.00

SB 0.58 0.61 0.55 0.55 0.42 0.64 0.73 0.66 0.70 0.81 0.53 0.48 0.67 1.00

DM 0.43 0.39 0.64 0.40 0.43 0.71 0.89 0.63 0.81 0.72 0.60 0.77 0.82 0.97 1.00

SM 0.53 0.54 0.76 0.58 0.88 0.69 0.80 0.56 0.79 0.77 0.54 0.69 0.83 0.61 0.87 1.00

GS 0.30 0.33 0.45 0.33 0.66 0.57 0.41 0.20 0.33 0.56 0.49 0.54 0.69 0.45 0.49 0.41 1.00

EP 0.41 0.48 0.60 0.49 0.42 0.22 0.69 0.40 0.78 0.51 0.45 0.41 0.59 0.59 0.66 0.79 0.71 1.00

GA 0.61 0.62 0.78 0.57 0.37 0.40 0.51 0.66 0.33 0.28 0.71 0.63 0.65 0.45 0.42 0.60 0.77 0.80 1.00

GB 0.59 0.64 0.59 0.68 0.63 0.70 0.66 0.59 0.61 0.69 0.78 0.42 0.63 0.93 0.82 0.69 0.51 0.68 0.44 1.00

GR 0.34 0.37 0.62 0.41 0.55 0.44 0.58 0.72 0.40 0.55 0.51 0.59 0.43 0.34 0.33 0.64 0.78 0.55 0.88 0.26 1.00

JN 0.39 0.36 0.25 0.22 0.21 0.57 0.46 0.80 0.59 0.41 0.33 0.48 0.50 0.66 0.86 0.23 0.39 0.77 0.51 0.69 0.38 1.00

GC 0.28 0.23 0.55 0.42 0.54 0.48 0.43 0.51 0.37 0.35 0.45 0.38 0.51 0.81 0.73 0.56 0.70 0.81 0.89 0.39 0.88 0.69 1.00

NW 0.88 0.80 0.62 0.86 0.59 0.80 0.29 0.77 0.48 0.80 0.85 0.49 0.81 0.88 0.85 0.58 0.66 0.71 0.45 0.93 0.40 0.74 0.31 1.00

DB 0.58 0.56 0.41 0.51 0.37 0.61 0.51 0.86 0.68 0.55 0.48 0.34 0.42 0.70 0.59 0.31 0.25 0.76 0.43 0.69 0.54 0.88 0.52 0.64 1.00

Margareth Gfrerer /BESSH--2016/Full Paper Proceeding Vol No-76, Issue 3, 1-10


ANALYSIS MODEL

Spatial Autocorrelation Test

To run the spatial regression analysis, the dependent variable

must be analyzed or draw a spatial autocorrelation. According to

the existing research results, home sales prices that are specified

in the dependent variable in this study, it is common to show the

spatial autocorrelation properties. To examine the data that are

used in this study whether show the same nature abovementioned

or not, analyze by drawing a map. As a result, it had been divided

high price areas and low price areas as a <Figure 5>.

Figure 4. Apartment price map of the research area

Therefore, the research area‟s housing value, it is determined that

there is a spatial dependency and would need more for the exact

analysis through Moran‟s I coefficient statistical analysis(Moran,

1950). The research data was tested for globally spatial clusters

through Moran‟s global clustering test to check whether spatial

autocorrelation exists. Global Moran‟s I can be found through

formula (1).

𝐼 =𝑛 𝑤𝑖 ,𝑗 𝑧𝑖𝑧𝑗

𝑛𝑗=1

𝑛𝑖=1

𝑆 𝑧𝑖2𝑛

𝑖=1

𝑤ℎ𝑒𝑟𝑒, 𝑆 = 𝑤𝑖 ,𝑗𝑛

𝑗=𝑖

𝑛

𝑖=1

(1)

Here, 𝑧𝑖 is the difference between the values of each feature and

the mean (𝑥𝑖 − 𝑋 ), while 𝑤𝑖 ,𝑗 represents the spatial dependency

between feature 𝑖 and 𝑗. 𝑛 Represents the number of all the

features. The index 𝐼 derived through this formula ranges from 0

to ±1 and the degree of spatially-correlation is stronger the closer

the index is to ±1 and away from 0 (Li et al, 2007).

In this formula, 𝑋 is a matrix of (𝑛 × 𝑘), 𝑌 is the (𝑛 × 1) vector

and 𝑊(𝑢𝑖 ,𝑣𝑖) is a matrix of (𝑛 × 𝑛). The diagonal elements in

𝑊(𝑢𝑖 ,𝑣𝑖) represent the geographical weights of centric

coordinate (𝑢𝑖 , 𝑣𝑖)‟s region 𝑖 and the adjacent 𝑛 observing points.

In GWR, 𝑊, the SWM, uses similar principles as the SWM used

to calculate Global Moran‟s I and Getis Ord G Index, but is

different as it is endogenously presumed.

Moran‟s I of the average sale price was calculated at 0.618 (Z-

score is 9.11 SD). Thus, it was possible to grasp that the high

level spatial dependence is shown.

Generating Spatial Weights Matrix(𝐖𝐮)

Taken together the results of the phenomenon analysis, not only

adjacency, but also other influences affect to the housing market

in Seoul. Therefore, It is not rational that calculate distance only

when generating the SWM for taking into account the spatial

effects. The new expression configured to solve these problems,

a <Formula 2> described below. From each nonnegative matrix

𝑊 = (𝑤𝑖𝑗 : 𝑖, 𝑗 = 1,2,… ,𝑛) is a possible SWM which

summarizes spatial relationships among 𝑛 spatial units.

𝑊𝑑 = (𝑤𝑖 ,𝑗 :𝑑𝑖𝑗−2)

(2)



42

𝑊𝑟 = (𝑤𝑖 ,𝑗 : each element in < 𝑇𝑎𝑏𝑙𝑒 3 >)

𝑊𝑢 = 𝑊𝑑 +𝑊𝑟

Focus on the <Formula 2>, which is for composition matrix𝑊𝑢 ,

some variations were applied to the conventional method. First,

obtain the original distance weighting matrix was names𝑊𝑑 . After

that utilizing the correlation coefficient of <Table 3> to make

housing price relational matrix. 𝑊𝑟 is calculated from row

standardization applied housing price relational matrix.𝑊𝑢 is

finally derivate summing 𝑊𝑑 and𝑊𝑟 , and conducted a row

standardization again. Calculation formula of row standardization

is <Formula 3>.

𝑤𝑖 ,𝑗𝑠 =𝑤𝑖 ,𝑗 𝑤𝑖 ,𝑗𝑗

(2)

Here, excluded self-explanation by assign that 𝑤𝑖𝑖 = 0 for all

𝑖 = 1,2,… ,𝑛. So 𝑊 has a zero diagonal element. Each element of

the 𝑊𝑢 is closer the distance between the apartment, and the

higher the correlation of changes in the buying and selling price,

with a greater value. The value of the case of the reverse is

lowered.

Applying Spatial Lag Model

<Formula 4> is basically accept the existing spatial lag model

utilizes 𝑊𝑢 calculated in <Formula 2>. The reason for using

spatial lag model is, in the study of Kim (2000), because it has

been demonstrated that already a spatial lag model in the housing

market of Seoul have explanatory power is superior to the spatial

error model. Spatial lag model assumed that affected not only the

explanatory variable of the internal housing prices in this area, but

also the price of the house neighbored region(Anselin, 1988).

Y = 𝜌𝑊𝑢𝑌 + 𝑋𝛽 + ϵ

𝑊ℎ𝑒𝑟𝑒,

𝑌:𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠

𝑋: 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠

𝑊𝑢 :𝑈𝑛𝑖𝑓𝑖𝑒𝑑 𝑆𝑊𝑀

𝜌,𝛽: 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑

𝜖: 𝑖. 𝑖.𝑑.

(4)

In this study, to adjust the ratio of the relative importance, from

(𝑑𝑖𝑠𝑡. 𝑖𝑚𝑝𝑜𝑟𝑡𝑎𝑛𝑐𝑒 ∶ 𝑐𝑜𝑟𝑟. 𝑖𝑚𝑝𝑜𝑟𝑡𝑎𝑛𝑐𝑒 = 0.2: 0.8)and

𝑐𝑜𝑟𝑟. 𝑖𝑚𝑝𝑜𝑟𝑡𝑎𝑛𝑐𝑒 𝑑𝑖𝑠𝑡. 𝑖𝑚𝑝𝑜𝑟𝑡𝑎𝑛𝑐𝑒 = 0.2: 0.8) be subjected to

analysis. At this time, the RMSE is to look for the best

combination of high explanatory power as finding the smallest.

The statistics to refer to in order to determine what method is

most effective in calculating the SWM is Akaike‟s Information

Criterion (AICc), and it is generally agreed that SWM with

minimal AICc is the best method (Fortheringham et al, 2002).

ANALYSIS RESULTS

Analysis, three models were performed, respectively. First is the

OLS analysis commonly used, Second, 𝑆𝐿𝑀𝑑 using distance

based SWM (𝑊𝑑 ), the third is a 𝑆𝐿𝑀𝑢 using Unified SWM (𝑊𝑢 ).

The first model has been added to clarify that to derive the results

of spatial regression was excellent much compared to the OLS.

The second model and the third model, by comparing both, were

analyzed separately in order to demonstrate the utility of 𝑊𝑢 .

Here, the weight of the correlation between the weights of the

physical distance, respectively 0.4:0.6. This decision was reason

in this way, will be described later.

Looking at the spatial regression analysis result of <Table 4>,

𝑆𝐿𝑀𝑢 shows the highest R-squared value and lower standard

error than the others (𝑂𝐿𝑆, 𝑆𝐿𝑀𝑑 ). Since the Durbin-Watson

numerical value has increased favorable direction, to 2, 𝑆𝐿𝑀𝑢 is

relatively free in multicollinearity problem. The spatial

coefficient is in 𝑆𝐿𝑀𝑑 displayed 0.384, in 𝑆𝐿𝑀𝑢 is 0.327. It

means that in 𝑆𝐿𝑀𝑢 , correlation effect became independent.

AICc values and Maximum likelihood based measure (ML)

represents the fit of the model 𝑆𝐿𝑀𝑢 is more suitable than 𝑆𝐿𝑀𝑑 .

Conventionally ML is larger, AICc is smaller means that the

model is appropriate.

As the individual variables point of view, whether the house's

location belongs to the U-City or not because it did not meet the

significance, it has been analyzed that does not have a significant

effect on the housing prices of up to now.

Another special variable, there is a need to look at the variables

age of the apartment. Because in OLS and 𝑆𝐿𝑀𝑑 analyses

demonstrated a positive sign, but in 𝑆𝐿𝑀𝑢 analysis, it was shown

a negative sign. Because the coefficient from 𝑆𝐿𝑀𝑢 does not

satisfy a significance level, so it is difficult to have a statistical

significance. However, it can put a meaning to the calibration

apartment variable in a common sense way while the process of

building the 𝑆𝐿𝑀𝑢 .



43

In this study, first, look at the correlation of the sales price for the

entire apartment complex in Seoul, and it was examined whether

can be explained only by the existing autoregression model. In the

result of the analysis, apartment transaction price could have been

formed not the specific phrase proximity only, but the some types

of correlation between specific districts also. In the existing

adjacency based SWM, it cannot reflect these correlations.

Because there can be described the effect on the area outside the

range of influence of the distance-decay function. To overcome

these limitations, we proposed a new method for creating SWM.

Next, calculate the RMSE for each model to statistically compare

the explanation power of the model. The result is 1.24 𝑆𝐿𝑀𝑑 and

𝑆𝐿𝑀𝑢 is calculated as 0.95. So, 𝑆𝐿𝑀𝑑 has a higher predictive

power than 𝑆𝐿𝑀𝑢 .

Like Abovementioned, the results of the spatial regression

(<Table 4>) has stated that using specific ratio between physical

distance and correlation coefficient. This is determined after

going change the relative weights of the two forces that are

TABLE IV

THE RESULT OF SPATIAL REGRESSION ANALYSIS

Variables

Standardized Coeff.

𝑂𝐿𝑆 𝑆𝐿𝑀𝑑 𝑆𝐿𝑀𝑢

Spatial Coefficient - 0.384**

0.327**

Intercept -51,928.2**

-62,151.4**

-57,837.3**

Physical

Character.

Rebuild. is Scheduled 0.019**

0.022**

0.022**

Total Buildings 0.107**

0.122**

0.123**

Area for Excl. Use 0.799**

0.594**

0.587**

Num. of Rooms -0.044**

-0.026**

-0.018**

Num. of Baths 0.007**

0.001**

0.002**

Total Household 0.035**

0.029**

0.028**

Parking Lot/HH 0.023**

0.028**

0.026**

Porch 0.027**

0.024**

0.024**

Aging of Apts. 0.094**

0.010**

-0.006**

Environ.

Character.

Dist. to General Hosp. -0.026**

-0.029**

-0.029**

Dist. to Pri. School -0.010**

-0.015**

-0.014**

Dist. to High School -0.033**

-0.037**

-0.039**

Dist. to Subway St. -0.116**

-0.104**

-0.105**

U-City Available 0.052**

0.048**

0.045**

Diagnosis

Values

Standard Error 20,589 17,047 15,680

D-W 1.58 1.62 1.71

R2 0.72 0.74 0.78

ML -23,056 -19,159 -17,233

AICc 39,593 36,101 34,816

**, *: .01 and .05 significance level, respectively



44

included in 𝑊𝑢 compares the fit of the model.

The standard error of the <table 5> is smallest when

(𝑑𝑖𝑠𝑡. 𝑖𝑚𝑝𝑜𝑟𝑡𝑎𝑛𝑐𝑒 ∶ 𝑐𝑜𝑟𝑟. 𝑖𝑚𝑝𝑜𝑟𝑡𝑎𝑛𝑐𝑒 = 0.4: 0.6) and r-

squared value is highest in the same condition. RMSE also

represents a similar flow. So we decided respectively 0.4 and 0.6

is the best ratio after several tests.

TABLE V

THE RESULT OF SPATIAL REGRESSION ANALYSIS

CONCLUSION

In this study, first, look at the correlation of the sales price for the

entire apartment complex in Seoul, and it was examined whether

can be explained only by the existing autoregression model. In the

result of the analysis, apartment transaction price could have been

formed not the specific phrase proximity only, but the some types

of correlation between specific districts also. In the existing

adjacency based SWM, it cannot reflect these correlations.

Because there can be described the effect on the area outside the

range of influence of the distance-decay function. To overcome

these limitations, we proposed a new method for creating SWM.

As a result of spatial regression analysis utilizing the new SWM

that reflects the price correlations, statistical significance was

higher relatively as compared with the Ordinary Least Square

(OLS) model. Further, it also had a smaller RMSE when using the

modified SWM, so it is verified the analysis results are

statistically valid. Thus, it is possible to conclude that real

explanatory power of SWM considering the correlation of price

fluctuations is stronger than existed simpler SWM such as

calculated from distance or adjacency only.

In addition, the best experimental result was derived from various

ratio attempt to change between physical distance significances

and relatively correlation significances. Result ratio is 0.4:0.6,

respectively. At those values, both fit and explanatory power were

the highest. Conversely, that the changes caused by other price-

related factors, such as Newtown construction or U-City

construction have accounted for 60 percent, it can be said quite

encouraging results.

However, it is limited in the fourth quarter of 2015 data used in

this study can point out the limitations that are close to almost

cross-section analysis. If it is possible to perform a future time

series analysis, will be able to SWM proposed in this study

receive a backing using a more robust model. Also, the analysis

did not reveal the source of the correlational effect can be pointed

out as well threshold. That is, another limitation of the analysis

was only revealed only how much correlated its influence and

there is missing detailed analysis.

ACKNOWLEDGMENT

This work is financially supported by Korea Minister of Ministry

of Land, Infrastructure and Transport (MOLIT) as 「 U-City

Master and Doctor Course Grant Program.

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Class Goodness of Fit

Physical

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2 RMSE

0.2 0.8 15,871 0.75 0.6

0.3 0.7 15,795 0.76 0.6

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0.8 0.2 16,253 0.72 0.2



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reconstitute spatial weights matrix...

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